Question

The difference in the measure of two complementary angles is given below. Find the measure of the angles. 12​

Answer 1

Let one angle be x.

This means that its complement is 90−x degrees.

But the difference in their measures is 12 degrees.

Therefore, you can write the equation:

x−(90−x)=12

Since the parentheses are preceded by a minus sign, you can remove the parentheses if you also change the signs of the terms inside the parentheses. Therefore, when you remove the parentheses

the equation becomes:

x−90+x=12

Combine the two x terms on the left side to get:

2x−90=12

Get rid of the −90 on the left side by adding 90 to both sides to get

2x=102

Solve for x by dividing both sides of the equation by 2 to get:

x=

2

102

=51

So, the measure of one of the two angles is 51 degrees. Its complement is the amount that

must be added to that angle such that this sum is 90 degrees. By subtracting 51 from 90

degrees, you find that the complement of the angle is an angle of 39 degrees.

Note that

the difference in the two angles is 51−39=12 degrees, just as the problem specified.

The answer to this problem is that the measures of the two complementary angles are 51

degrees and 39 degrees.

Hence, this is the answer.